Here, the parameter \(\beta > 0\)  is the limiting aspect ratio of the data; thus for \(\beta = 1\) , the matrices are effectively square for all large \(n\) . Baik and Silverstein [1]} and Paul [2]} find the limits of leading eigenvalues in the spiked covariance model, which is closely related to model (REF ).
Benaych-Georges and Rao Nadakuditi [3]} derive asymptotic properties of the empirical singular value decomposition of \(\widetilde{X}_n\)  (details of model (REF ) are provided in Section REF ). Two phenomena arise not present in classical fixed-\(n\)  asymptotics:
